# Anti-concentration and honest, adaptive confidence bands

@article{Chernozhukov2013AnticoncentrationAH, title={Anti-concentration and honest, adaptive confidence bands}, author={Victor Chernozhukov and Denis Chetverikov and Kengo Kato}, journal={arXiv: Statistics Theory}, year={2013} }

Modern construction of uniform confidence bands for nonparametric densities (and other functions) often relies on the classical Smirnov-Bickel-Rosenblatt (SBR) condition; see, for example, Gin\'{e} and Nickl [Probab. Theory Related Fields 143 (2009) 569-596]. This condition requires the existence of a limit distribution of an extreme value type for the supremum of a studentized empirical process (equivalently, for the supremum of a Gaussian process with the same covariance function as that of…

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Anti-concentration and honest, adaptive confidence bands

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Modern construction of uniform confidence bands for non-parametric densities (and other functions) often relies on the classical Smirnov-Bickel-Rosenblatt (SBR) condition; see, for example, Gine and…

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